Extracting analytical nonlinear models from analog circuits by recursive vector fitting of Transfer Function Trajectories

This paper presents a technique for automatically extracting analytical behavioral models from the netlist of a nonlinear analog circuit. Subsequent snapshots of the internal circuit Jacobian are sampled during time-domain analysis and are then processed into Transfer Function Trajectories (TFT). The TFT data project the nonlinear dynamics of the system onto a hyperplane in the mixed state-space/frequency domain. Next Recursive Vector Fitting (RVF) algorithm is used to extract an analytical Hammerstein model out of the TFT data in an automated fashion. The resulting RVF model equations are implemented as an accurate nonlinear behavioral model in the time domain. The model is guaranteed stable by construction and can trade off complexity for accuracy. The technique is validated on a high-speed analog buffer circuit containing 70 linear and nonlinear components, showing a 7X speedup.